Implementation of sparse matrix algorithms in an advection-diffusion-chemistry module

Authors:
Krassimir Georgiev;Zahari Zlatev
Affiliations:
Institute for Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113-Sofia, Bulgaria;National Environmental Research Institute, Aarhus University Frederiksborgvej 399, P. O. 358, DK-4000 Roskilde, Denmark
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

A two-dimensional advection-diffusion-chemistry module of a large-scale environmental model is taken. The module is described mathematically by a system of partial differential equations. Sequential splitting is used in the numerical treatment. The non-linear chemistry is most time-consuming part and it is handled by six implicit algorithms for solving ordinary differential equations. This leads to the solution of very long sequences of systems of linear algebraic equations. It is crucial to solve these systems efficiently. This is achieved by applying four different algorithms. The numerical results indicate that the algorithms based on a preconditioned sparse matrix technique and on a specially designed algorithm for the particular problem under consideration perform best.